library(ggplot2)


#Example 1: Is the proportion of baby boys born different than 0.5?  
#           Is it different from the proportion of baby girls?

#Visualize/Format Data
total<-1000
boys <-584
girls<-total-boys
ds1.1<-data.frame(category=c("boys", "constant"), proportion=c(boys/total, 0.5))
barplot(proportion~category, col=c("blue","grey"), data=ds1, xlab="Boys versus Constant")+box()

ds1.2<-data.frame(category=c("boys", "girls"), proportion=c(boys/total, girls/total))
barplot(proportion~category, col=c("blue","pink"), data=ds1.2, xlab="Boys versus Girls")+box()

#One-Sample Test
f1.1<-prop.test(x=584, n=1000, p=0.50, alternative="two.sided")
f1.1

#Two-Sample Test
f1.2<-prop.test(c(boys,girls), c(total,total), alternative ="two.sided")
f1.2

#Graphs
plot(1, f1.1$estimate, ylim=c(0,1), axes=F, xlab="Boys", ylab="Proportion")
axis(side=1, at=1, cex.lab=1.5, cex.axis=1.2, labels="")
axis(2, at=c(0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0), las=2, cex.lab=1.5, cex.axis=0.80)
arrows(1, f1.1$conf.int[1], 1, f1.1$conf.int[2],length=0.05, angle=90, code=3)
abline(h=0.5, col="red")
box()

diff<-f1.2$estimate[1]-f1.2$estimate[2]
plot(1, diff, ylim=c(0,1), axes=F, xlab="Difference between Boys and Girls", ylab="Proportion")
axis(side=1, at=1, cex.lab=1.5, cex.axis=1.2, labels="")
axis(2, at=c(0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0), las=2, cex.lab=1.5, cex.axis=0.80)
arrows(1, f1.2$conf.int[1], 1, f1.2$conf.int[2],length=0.05, angle=90, code=3)
abline(h=0.0, col="red")
box()


################################################################################


#Example 2: Is there a significant association between Treatment Status (Treatment=T, Control=C)
#           and Disease Outcome (Cured=1, Not-cured=0)?

#Visualize/Format Data
ds2 <- matrix(c(15,3,5,19), nrow = 2)
colnames(ds2) <- c("Treat", "Control")
rownames(ds2)  <- c("Cured", "Not")
ds2

#Chi-Square test of Independence
f2.1<-chisq.test(ds2) #some cells <5
f2.1

#Fisher's Exact Test
f2.2<-fisher.test(ds2)
f2.2

#Graph
mosaicplot(ds2, color=T)


################################################################################


#Example 3: Are the phenotype ratios for a sample of pea plants equal to the hypothesized 9:3:3:1?

#Visualize/Format Data
observed <-c(56,13,15,7)
expected <-c(9/16,3/16,3/16,1/16)

ds3 <- matrix(c(observed,expected), nrow = 4)
colnames(ds3) <- c("Observed", "Expected")
rownames(ds3)  <- c("AB", "Ab", "aB", "aa")
ds3

#Chi-square goodness of fit
f3.1<-chisq.test(x=observed, p=expected)
f3.1

#Graph
ds3.2 <-data.frame(type=c(rep("Observed",4),rep("Expected",4)),
                  genotype=c(rep(c("AB","Ab","aB","ab"),2)),
                  proportion=c(observed/sum(observed),expected))
                    
ggplot(data=ds3.2, aes(x=genotype, y=proportion)) +
  geom_bar(aes(fill=type), stat="identity", position=position_dodge())